In this section, we provide experimental results of Algorithm . We develop a Julia implementation [1]}; and we consider solving problems in CUTEst test set [2]}, in particular using problems BYRDSPHR, HS7, HS48 as examples to validate our main theoretical results. For each problem, we perform \(10^5\)  SQP iterations and, in each iteration, we perform 50 randomized Kaczmarz iterations for solving the Newton system. That is, for each \(t\) , we let \(S_{t,j}\stackrel{iid}{\sim } \text{Uniform}\lbrace _1,\ldots ,_{m+d}\rbrace \)  for \(j=1,\ldots ,50\) , and perform the iteration (REF ) with \({z}_{t,0} = {0}\) . The true solution of each problem is solved by applying IPOPT solver [3]}. See a Julia implementation of the solver at https://github.com/jump-dev/Ipopt.jl.
